Resources for developing mathematical thinking as a self-learner?
To begin with, I apologize if this sounds stupid. I already feel like an idiot writing this.
I'm studying at a university in Germany, bachelors, and I used to think I disliked mathematics. But I've realized that I actually enjoy it once I sit down and start trying to solve problems.
My main problem is that after a few months, I tend to forget what I've learned. I know repetition is important, but I feel like the bigger issue is that I often learn how to use an equation without really understanding what's behind it. That is the problem.
I come from Central Asia, where I feel like I've always been surrounded by people who are extremely good at mathematics. Because of that, I've often felt like I'm simply not naturally good at it.
Recently, though, I've realized that I actually enjoy the process of solving mathematical problems and puzzles. I want to develop that way of thinking rather than just memorize formulas and procedures.
I've found these books:
- Book of Proof — Richard Hammack
- How to Prove It — Daniel J. Velleman
- Mathematical Thinking: Problem-Solving and Proofs — John P. D'Angelo & Douglas B. West
- Concrete Mathematics — Graham, Knuth & Patashnik
Would these be a good approach for someone in my situation? Are there other books or resources you'd recommend for developing mathematical intuition, reasoning, and problem-solving ability?